In parallelogram ABCD, m<A = x ^2+ 8x – 21 and m<C = 5x + 33. Find m<B.

Question

In parallelogram ABCD, m<A = x ^2+ 8x – 21 and m<C = 5x + 33. Find m<B.

Answer 1

In a parallelogram opposite angles are equal. Since <A and <C are opposite angles we can equate their two measures and solve for x:

x^2 + 8x -21 = 5x + 33

x^2 + 3x - 54 = 0

(x+9)(x-6) = 0

x = -9 or 6

x = 6 is only valid value

m<C = 5x+33 = 5*6 + 33 = 63

In a parallelogram consecutive angles are supplementary. <C and <B are supplementary, which means their measures add up to 180 degrees so:

m<C + m<B = 180

63 + m<B = 180

m<B = 117